Airborne, ground, marine and downhole magnetic measurements have played an important role in detection of magnetic targets such as land mines, naval mines, submarines, shipwrecks, unexploded ordnance (UXO), archaeological artefacts and structures, buried drums containing, for example, toxic waste, ferrous particles in food and hospital laundry, and many others. Magnetic surveys also have major applications to mapping geology, in exploration for minerals and energy resources, and in environmental and archaeological surveys. Total magnetic intensity (TMI) sensors may be used in such surveys. However, limiting factors when using TMI sensors include complicating effects of the orientation of the geomagnetic field, which produces asymmetric anomalies that are displaced from source locations, the sensitivity of the shape and strength of TMI anomalies to direction of source magnetisation, relatively low resolution compared to magnetic field gradients, frequent need for post-processing techniques, and the fact that only a limited, distorted and fuzzy view of geology or terrain is obtained due to cost constraints on sampling density. Moreover, it is not possible to locate targets uniquely between survey lines or to delineate adversely oriented structures in low latitudes near the Earth's equator.
Magnetic surveys using vector magnetometers such as fluxgate-based or SQUID-based detectors have also been considered, because of the extra information that is in principle obtainable from measuring three components of the field, rather than a single TMI component. Vector surveys, where the direct measurement of vector components has been attempted, have met with mixed success. The accuracy of direct measurement of the field vector is largely governed by orientation errors, which are generally so large that the theoretical derivation of the components from sufficiently densely sampled TMI is actually preferable. Vector magnetometry is so sensitive to orientation errors because the anomalies that need to be detected are usually very weak compared to the background geomagnetic field. For example a 1° change in orientation produces changes in vector components of the geomagnetic field of up to approximately 1000 nT, whereas anomalies are often of the order of a few nT, or even sub nanoTesla.
An important application of magnetic sensors is the detection, location and classification (DLC) of magnetic objects. Compact magnetic bodies can be well represented by a point dipole source, except very close to the body. A number of methods have been proposed for locating dipole targets from magnetic gradient tensor data. Some of these methods are based on point-by-point analysis of the eigenvectors of the tensor, and are adversely affected by noise in individual measurements of the gradient tensor elements. Calculated eigenvectors are inherently sensitive to noise in gradient tensor elements and eigenvector-based methods may not always be robust. If two eigenvalues are almost equal, for example, small perturbations of the eigenvalues can produce approximately 90° jumps in the corresponding eigenvector orientations. Methods that rely on recalculation of tensor elements with respect to principal axes of the tensor (which are defined by the eigenvectors) also suffer from this problem. Moreover, as the analysis is essentially point-by-point, the solutions are unreliable for individually noisy tensor measurements.
Furthermore, there is an inherent four-fold ambiguity in obtaining solutions for dipole location and orientation of its moment from point-by-point analysis of gradient tensors, which must be resolved by comparing solutions from different sensor locations, rejecting those that are not consistent (the so-called “ghost” solutions) and retaining the solutions that exhibit the best clustering. Existing methods of dipole tracking are also not robust to the contamination of the measured signal by variable background gradients, interfering anomalies, instrument drift or departures of the target from a pure dipole source.
Proposed methods for resolving ambiguity of gradient tensor measurements by eliminating ghost solutions rely on numerical differentiation of gradient tensor time-series to obtain gradient rate tensors, or by using arrays of triaxial magnetometers that constitute two or more tensor gradiometers with small spatial separation. Both approaches effectively amount to incorporating second order gradients of magnetic components into the analysis, which are more subject to noise than the first order gradient tensor. Furthermore, the incorporation of higher order gradient information greatly increases the mathematical complexity and computational demands of the solutions, making near real-time tracking difficult. Moreover, numerical differentiation amplifies noise in the original data, and the gradient rate tensor has a l/r5 fall-off, which makes the signal very weak, except very close to the source.
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